General Solutions of Trigonometric Equations
There are a few methods that can be used to solve trigonometric equations. One method is to use inverse trigonometric functions. Another method is to use the quadratic formula.
To solve a trigonometric equation using inverse trigonometric functions, first rewrite the equation in terms of inverse functions. For example, if the equation is sin(x) = 1, rewrite it as sin(x) = inverse_cos(x).
Next, use inverse functions to solve for x. In the example equation, this would mean solving for x in terms of inverse cosine. The solution would be x = arcsin(1/cos(x)).
To solve a trigonometric equation using the quadratic formula, first rewrite the equation in terms of square roots. For example, if the equation is sin(x) = 1, rewrite it as sin(x) = sqrt(1).
Next, use the quadratic formula to solve for x. In the example equation, this would mean solving for x in terms of square roots. The solution would be x = (-1 ± sqrt(1 – 4))/2.
Proofs for Solutions of Trigonometric Equations
There are a few different methods that can be used to solve trigonometric equations. One method is to use the quadratic equation. Another is to use trigonometric identities.
The quadratic equation can be used to solve trigonometric equations when they can be reduced to the form:
\[a\cos ^2x+b\sin ^2x=c\]
This equation can be solved by using the Quadratic Formula.
Another method for solving trigonometric equations is to use trigonometric identities. Some of the more common identities that can be used are:
\[sin ^2x+cos ^2x=1\]
\[sin x=cos ^2x\]
\[cos x=sin ^2x\]
These identities can be used to solve trigonometric equations by canceling out the squares on the left-hand side of the equation.
Also Read | Subject Wise Formulas List
